public static double KVA(DateTime originDate, DateTime[] ExEDates, double[] CapExposures, IIrCurve fundingCurve)
{
if (ExEDates.Length != CapExposures.Length)
{
throw new Exception("Number of exposure dates and values must be equal");
}
var lastDate = originDate;
var kva = 0.0;
for (var i = 0; i < ExEDates.Length; i++)
{
if (ExEDates[i] < originDate)
{
continue;
}
var fwdDf = fundingCurve.GetDf(lastDate, ExEDates[i]);
var df = fundingCurve.GetDf(originDate, ExEDates[i]);
kva += CapExposures[i] / fwdDf * df;
lastDate = ExEDates[i];
}
return(kva);
}
public static (double FBA, double FCA) FVA(DateTime originDate, DateTime[] ExEDates, double[] EPEExposures, double[] ENEExposures, HazzardCurve hazzardCurve, IIrCurve discountCurve, IIrCurve fundingCurve)
{
if (ExEDates.Length != EPEExposures.Length)
{
throw new Exception("Number of EPE dates and EPE values must be equal");
}
if (ExEDates.Length != ENEExposures.Length)
{
throw new Exception("Number of ENE dates and ENE values must be equal");
}
var lastDate = originDate;
var fba = 0.0;
var fca = 0.0;
for (var i = 0; i < ExEDates.Length; i++)
{
if (ExEDates[i] < originDate)
{
continue;
}
var pSurvival = hazzardCurve.GetSurvivalProbability(lastDate, ExEDates[i]);
var fwdDf = fundingCurve.GetDf(lastDate, ExEDates[i]) / discountCurve.GetDf(lastDate, ExEDates[i]);
var df = fundingCurve.GetDf(originDate, ExEDates[i]);
fba += ENEExposures[i] * pSurvival / fwdDf * df;
fca += EPEExposures[i] * pSurvival / fwdDf * df;
lastDate = ExEDates[i];
}
return(fba, fca);
}
public static double PvProfile(DateTime originDate, DateTime[] exposureDates, double[] exposures, IIrCurve discountCurve)
{
var capital = 0.0;
var time = 0.0;
if (exposureDates.Length != exposures.Length || exposures.Length < 1)
{
throw new DataMisalignedException();
}
if (exposureDates.Length == 1)
{
return(discountCurve.GetDf(originDate, exposureDates[0]) * exposures[0]);
}
for (var i = 0; i < exposureDates.Length - 1; i++)
{
var exposure = (exposures[i] + exposures[i + 1]) / 2.0;
var df = discountCurve.GetDf(originDate, exposureDates[i + 1]);
var dt = exposureDates[i].CalculateYearFraction(exposureDates[i + 1], DayCountBasis.ACT365F);
capital += exposure * dt * df;
time += dt;
}
return(capital / time);
}
public double PV_SmallSteps(HazzardCurve hazzardCurve, IIrCurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true)
{
var nodeDates = DatePeriodType.M.GenerateDateSchedule(hazzardCurve.OriginDate, FinalSensitivityDate);
//contingent leg
var pv = 0.0;
for (var i = 1; i < nodeDates.Length; i++)
{
pv += discountCurve.GetDf(discountCurve.BuildDate, nodeDates[i])
* hazzardCurve.GetDefaultProbability(nodeDates[i - 1], nodeDates[i]);
}
pv *= (1.0 - recoveryRate) * Notional;
//fixed leg
foreach (var f in FixedSchedule.Flows)
{
pv -= f.Notional * f.YearFraction * Spread * discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate) * hazzardCurve.GetSurvivalProbability(f.SettleDate);
if (payAccruedOnDefault)
{
pv -= 0.5 * f.Notional * f.YearFraction * Spread
* hazzardCurve.GetDefaultProbability(f.AccrualPeriodStart, f.AccrualPeriodEnd)
* discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate);
}
}
return(pv);
}
public double PV_LinearApprox(HazzardCurve hazzardCurve, IIrCurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true)
{
var nodeDates = DatePeriodType.M.GenerateDateSchedule(hazzardCurve.OriginDate, FinalSensitivityDate);
var ts = nodeDates.Select(d => discountCurve.BuildDate.CalculateYearFraction(d, DayCountBasis.ACT365F)).ToArray();
var integrandD = new Func <DateTime, double> (d => discountCurve.GetDf(discountCurve.BuildDate, d) * -hazzardCurve.GetSurvivalProbabilitySlope(d));
var integrandT = new Func <double, double>(t => integrandD(OriginDate.AddYearFraction(t, DayCountBasis.ACT365F)));
//contingent leg
var pv = (1.0 - recoveryRate) * Notional * Integration.SimpsonsRuleExtended(integrandT, 0, ts.Last(), 100);
//fixed leg
foreach (var f in FixedSchedule.Flows)
{
pv -= f.Notional * f.YearFraction * Spread * discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate) * hazzardCurve.GetSurvivalProbability(f.SettleDate);
if (payAccruedOnDefault)
{
pv -= 0.5 * f.Notional * f.YearFraction * Spread
* hazzardCurve.GetDefaultProbability(f.AccrualPeriodStart, f.AccrualPeriodEnd)
* discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate);
}
}
return(pv);
}
public static double CVA(DateTime originDate, DateTime[] EPEDates, double[] EPEExposures, HazzardCurve hazzardCurve, IIrCurve discountCurve, double LGD)
{
if (EPEDates.Length != EPEExposures.Length)
{
throw new Exception("Number of EPE dates and EPE values must be equal");
}
var lastDate = originDate;
var cva = 0.0;
for (var i = 0; i < EPEDates.Length; i++)
{
if (EPEDates[i] < originDate)
{
continue;
}
var pDefault = hazzardCurve.GetDefaultProbability(lastDate, EPEDates[i]);
var df = discountCurve.GetDf(originDate, EPEDates[i]);
cva += EPEExposures[i] * pDefault * df * LGD;
lastDate = EPEDates[i];
}
return(-cva);
}
public double RiskyDiscountFactor(DateTime startDate, DateTime endDate, IIrCurve discountCurve, double LGD)
{
var dp = GetDefaultProbability(startDate, endDate);
var el = dp * LGD;
var df = discountCurve.GetDf(startDate, endDate);
return((1.0 - el) * df);
}
public static double SwapPv(IPriceCurve priceCurve, AsianSwapStrip swap, IIrCurve discountCurve)
{
var swapletPVs = swap.Swaplets.Select(s =>
(priceCurve.GetAveragePriceForDates(s.FixingDates.AddPeriod(RollType.F, s.FixingCalendar, s.SpotLag)) - s.Strike)
* (s.Direction == TradeDirection.Long ? 1.0 : -1.0)
* discountCurve.GetDf(priceCurve.BuildDate, s.PaymentDate));
return(swapletPVs.Sum());
}
public static IrCurve StripFxBasisCurve(string cmeFwdFileName, string ccyPair, Currency curveCcy, string curveName, DateTime valDate, IIrCurve baseCurve)
{
var fwds = GetFwdFxRatesFromFwdFile(cmeFwdFileName, ccyPair);
var dfs = fwds.ToDictionary(f => f.Key, f => fwds[valDate] / f.Value * baseCurve.GetDf(valDate, f.Key));
if (ccyPair.EndsWith("USD")) //flip dfs
{
dfs = dfs.ToDictionary(x => x.Key, x => 1.0 / x.Value);
}
var pillars = dfs.Keys.OrderBy(k => k).ToArray();
var dfsValues = pillars.Select(p => dfs[p]).ToArray();
var curve = new IrCurve(pillars, dfsValues, valDate, curveName, Interpolator1DType.Linear, curveCcy, null, RateType.DF);
return(curve);
}
//http://www.bnikolic.co.uk/cds/cdsvaluation.html
//var contingentLeg = (1.0 - recoveryRate) *
public double PV_PiecewiseFlat(HazzardCurve hazzardCurve, IIrCurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true)
{
var nodeDates = FixedSchedule.Flows.Select(f => f.AccrualPeriodEnd).ToArray();
var pv = 0.0;
//contingent leg
var d = hazzardCurve.OriginDate;
foreach (var nd in nodeDates)
{
var deltaT = d.CalculateYearFraction(nd, hazzardCurve.Basis);
var s = hazzardCurve.GetSurvivalProbability(d);
var dd = discountCurve.GetDf(discountCurve.BuildDate, d);
var lambda = System.Math.Log(s / hazzardCurve.GetSurvivalProbability(nd)) / deltaT;
var f = System.Math.Log(dd / discountCurve.GetDf(discountCurve.BuildDate, nd)) / deltaT;
var term1 = (lambda == 0 && f == 0) ? 1.0 : lambda / (lambda + f);
pv += term1 * (1.0 - System.Math.Exp(-deltaT * (lambda + f))) * s * dd;
d = nd;
}
pv *= (1.0 - recoveryRate) * Notional;
//fixed leg
foreach (var f in FixedSchedule.Flows)
{
pv -= f.Notional * f.YearFraction * Spread * discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate) * hazzardCurve.GetSurvivalProbability(f.SettleDate);
if (payAccruedOnDefault)
{
pv -= 0.5 * f.Notional * f.YearFraction * Spread
* hazzardCurve.GetDefaultProbability(f.AccrualPeriodStart, f.AccrualPeriodEnd)
* discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate);
}
}
return(pv);
}
